Co-Representation Neural Hypergraph Diffusion for Edge-Dependent Node Classification

Hypergraphs are widely employed to represent complex higher-order relationships in real-world applications. Most hypergraph learning research focuses on node- or edge-level tasks. A practically relevant but more challenging task, edge-dependent node classification (ENC), is only recently proposed. In ENC, a node can have different labels across different hyperedges, which requires the modeling of node-hyperedge pairs instead of single nodes or hyperedges. Existing solutions for this task are based on message passing and model within-edge and within-node interactions as multi-input single-output functions. This brings three limitations: (1) non-adaptive representation size, (2) node/edge agnostic messages, and (3) insufficient interactions among nodes or hyperedges. To tackle these limitations, we develop CoNHD, a new solution based on hypergraph diffusion. Specifically, we first extend hypergraph diffusion using node-hyperedge co-representations. This extension explicitly models both within-edge and within-node interactions as multi-input multi-output functions using two equivariant diffusion operators. To avoid handcrafted regularization functions, we propose a neural implementation for the co-representation hypergraph diffusion process. Extensive experiments demonstrate the effectiveness and efficiency of the proposed CoNHD model.